Its not really that hard to explain..
It will only benefit superchargers that are oil cooled, It will also only benefit turbo's that are oil cooled.
The shafts on most turbo chargers spin really really really fast (up to 50,000 RPM's).. Therefore, it cause alot of heat. To keep the heat level down, they are cooled by either oil or coolant. The shaft has no "brake" or anyway of stopping at will, it just slows down until it completely stops. Therefore, when you drive hard and its spinning fast, and you just shut your car off, it still spins but no oil or coolant is circulating around it. If that happens, the oil around the shaft just sits there and can cause it to "cok". "Coking" means the oil will basically bake and turn into a hard substance.. *I know, BAD!*
So back to what the turbo timer does.. It keeps your car running when you turn the key off, enough time to let the turbo cool down. Usually about 1 minute per hour of driving.